Rewrite as a simplified fraction. ${1.75\overline{1} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1751.1111...\\ 100x &= 175.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1576}$ ${x = \dfrac{1576}{900}} $ ${x = \dfrac{394}{225}} \text{or} {1 \dfrac{169}{225}}$